Superstatistical energy distributions of an ion in an ultracold buffer gas

An ion in a radiofrequency ion trap interacting with a buffer gas of ultracold neutral atoms is a driven dynamical system which has been found to develop a non-thermal energy distribution with a power law tail. The exact analytical form of this distribution is unknown, but has often been represented empirically by q-exponential (Tsallis) functions. Based on the concepts of superstatistics, we introduce a framework for the statistical mechanics of an ion trapped in an RF field subject to collisions with a buffer gas. We derive analytic ion secular energy distributions from first principles both neglecting and including the effects of the thermal energy of the buffer gas. For a buffer gas with a finite temperature, we prove that Tsallis statistics emerges from the combination of a constant heating term and multiplicative energy fluctuations. We show that the resulting distributions essentially depend on experimentally controllable parameters paving the way for an accurate control of the statistical properties of ion-atom hybrid systems.Comment: Main text 6 pages, 4 figures. Total length including supplemental material 11 pages, 6 figure

The energy distribution of an ion in a radiofrequency trap interacting with a nonuniform neutral buffer gas

An ion in a radiofrequency (rf) trap sympathetically cooled by a simultaneously trapped neutral buffer gas exhibits deviations from thermal statistics caused by collision-induced coupling of the rf field to the ion motion. For a uniform density distribution of the buffer gas, the energy distribution of the ion can be described by Tsallis statistics. Moreover, runaway heating of the ion occurs if the buffer gas particles are sufficiently heavy relative to the ion. In typical experiments, however, ultracold buffer gases are confined in traps resulting in localised, non-uniform density distributions. Using a superstatistical approach, we develop an analytical model for an ion interacting with a localised buffer gas. We demonstrate theoretically that limiting collisions to the centre of the ion trap enables cooling at far greater mass ratios than achievable using a uniform buffer gas, but that an upper limit to the usable mass ratio exists even in this case. Furthermore, we analytically derive the energy distribution for an ion interacting with a buffer gas held in a harmonic potential. The analytical distribution obtained is found to be in excellent agreement with the results of numerical simulations.Comment: 27 pages, 6 figure

Superstatistical velocity distributions of cold trapped ions in molecular dynamics simulations

We present a realistic molecular-dynamics treatment of laser-cooled ions in radiofrequency ion traps which avoids previously made simplifications such as modeling laser cooling as a friction force and combining individual heating mechanisms into a single effective heating force. Based on this implementation, we show that infrequent energetic collisions of single ions with background gas molecules lead to pronounced heating of the entire ion ensemble and a time-varying secular ensemble temperature which manifests itself in a superstatistical time-averaged velocity distribution of the ions. The effect of this finding on the experimental determination of ion temperatures and rate constants for cold chemical reactions is discussed.Comment: 13 pages, 12 figures, accepted for publication in Phys. Rev.

Energy distributions of an ion in a radiofrequency trap immersed in a buffer gas under the influence of additional external forces

An ion held in a radiofrequency trap interacting with a uniform buffer gas of neutral atoms develops a steady-state energy distribution characterised by a power-law tail at high energies instead of the exponential decay characteristic of thermal equilibrium. We have previously shown that the Tsallis statistics frequently used as an empirical model for this distribution is a good approximation when the ion is heated due to a combination of micromotion interruption and exchange of kinetic energy with the buffer gas [I. Rouse and S. Willitsch, Phys. Rev. Lett. 118, 143401 (2017)]. Here, we extend our treatment to include the heating due to additional motion of the ion caused by external forces, including the "excess micromotion" induced by uniform electric fields and rf phase offsets. We show that this also leads to a Tsallis distribution with a potentially different power-law exponent from that observed in the absence of this additional forced motion, with the difference increasing as the ratio of the mass of the neutral atoms to that of the ion decreases. Our results indicate that unless the excess micromotion is minimised to a very high degree, then even a system with very light neutrals and a heavy ion does not exhibit a thermal distribution.Comment: 16 pages, 9 figure

Applied regional monitoring of the vernal advancement and retrogradation (Green wave effect) of natural vegetation in the Great Plains corridor

The author has identified the following significant results. LANDSAT 2 has shown that digital data products can be effectively employed on a regional basis to monitor changes in vegetation conditions. The TV16 was successfully applied to an extended test site and the Great Plains Corridor in tests of the ability to assess green forage biomass on rangelands as an index to vegetation condition. A strategy for using TV16 on a regional basis was developed and tested. These studies have shown that: (1) for rangelands with good vegetative cover, such as most of the Great Plains, and which are not heavily infested with brush or undesirable weed species, the LANDSAT digital data can provide a good estimate (within 250 kg/ha) of the quantity of green forage biomass, and (2) at least five levels of pasture and range feed conditions can be adequately mapped for extended regions

BIOLOGICAL PURIFICATION OF GROUNDWATER POLLUTED WITH NITROGENOUS COMPOUNDS

Joint Research on Environmental Science and Technology for the Eart

Experimental and numerical investigation of interface damage in composite L-angle sections under four-point bending

© The Author(s) 2020. Curved laminates in aero-structures, such as the L-angle sections where webs and flanges meet, are prone to delamination due to high interlaminar stresses in these regions. Some efforts to investigate delamination in these structures can be found in the literature but commonly structures are limited to unidirectional layups or modelling approaches are constrained to the cohesive element based methods. In this work, multi-directional L-angle laminates were manufactured using unidirectional prepregs and tested under four-point bending load conditions to examine the interface damage. Acoustic emission technique was used to assist the capture of damage initiation and propagation. Three interface modelling strategies for predicting delamination, namely cohesive element, cohesive surface and perfectly bonded interface were used in the numerical study. The interface damage behaviour was successfully predicted by the simulation methods and differences among the strategies were compared

Scaling dependence on the fluid viscosity ratio in the selective withdrawal transition

In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance S above a two-fluid interface. At sufficiently low withdrawal rates, Q, the interface forms a steady state hump and only the upper fluid is withdrawn. When Q is increased (or S decreased), the interface undergoes a transition so that the lower fluid is entrained with the upper one, forming a thin steady-state spout. Near this transition the hump curvature becomes very large and displays power-law scaling behavior. This scaling allows for steady-state hump profiles at different flow rates and tube heights to be scaled onto a single similarity profile. I show that the scaling behavior is independent of the viscosity ratio.Comment: 33 Pages, 61 figures, 1 tabl

Opportunity or dead end? Rethinking the study of entrepreneurial action without a concept of opportunity

This article has two objectives: to critique the dominant opportunity discovery and creation literatures and to propose a new, critical realist–inspired analytical framework to theorise the causes, processes and consequences of entrepreneurial action – one that needs no concept of opportunity. We offer three reasons to support our critique of opportunity studies. First, there are important absences, contradictions and inconsistencies in definitions of opportunity in theoretical and empirical work that mean the term cannot signal a clear direction for theorising or empirical research. Our central criticism is that the concept of opportunity cannot refer simultaneously, without contradiction, to a social context offering profit-making prospects, to particular practices and to agents’ subjective beliefs or imagined futures. Second, a new definition of opportunity would perpetuate the conceptual chaos. Third, useful concepts to capture important entrepreneurial processes are readily available, for instance, combining resources, creating new ventures and achieving product sales, which render a concept of opportunity superfluous. Instead, we conceptualise entrepreneurial action as investments in resources intended to create new goods and services for market exchange emergent from the interaction between agential, socialstructural and cultural causal powers

High and low molecular weight crossovers in the longest relaxation time dependence of linear cis-1,4 polyisoprene by dielectric relaxations

The dielectric relaxation of cis-1,4 Polyisoprene [PI] is sensitive not only to the local and segmental dynamics but also to the larger scale chain (end-to-end) fluctuations. We have performed a careful dielectric investigation on linear PI with various molecular weights in the range of 1 to 320 kg/mol. The broadband dielectric spectra of all samples were measured isothermally at the same temperature to avoid utilizing shift factors. For the low and medium molecular weight range, the comparisons were performed at 250 K to access both the segmental relaxation and normal mode peaks inside the available frequency window (1 mHz–10 MHz). In this way, we were able to observe simultaneously the effect of molecular mass on the segmental dynamics—related with the glass transition process—and on the end-to-end relaxation time of PI and thus decouple the direct effect of molecular weight on the normal mode from that due to the effect on the monomeric friction coefficient. The latter effect is significant for low molecular weight (M w < 33 kg/mol), i.e., in the range where the crossover from Rouse dynamics to entanglement limited flow occurs. Despite the conductivity contribution at low frequency, careful experiments allowed us to access to the normal mode signal for molecular weights as high as M w = 320 kg/mol, i.e., into the range of high molecular weights where the pure reptation behavior could be valid, at least for the description of the slowest chain modes. The comparison between the dielectric relaxations of PI samples with medium and high molecular weight was performed at 320 K. We found two crossovers in the molecular weight dependence of the longest relaxation time, the first around a molecular weight of 6.5 ± 0.5 kg/mol corresponding to the end of the Rouse regime and the second around 75 ± 10 kg/mol. Above this latter value, we find a power law compatible with exponent 3 as predicted by the De Gennes theory